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There are 2 types of additional coverages beyond basic liability coverage:
uninsured motorist coverage, and
underinsured motorist coverage
The claims person told me that the uninsured motorist coverage would not be applicable in this case because the other driver fled and we don't know if the other driver has insurance?
An 'uninsured motorist clause'
is a provision commonly found in US auto insurance policies that provides for a driver to receive damages for any injury he or she receives from an uninsured, negligent driver. The owner of the policy pays a premium to the insurance company to include this clause. Although not exclusive, this coverage is typically added to an automobile insurance policy. In the event of a qualifying accident, the insurance company pays the difference between what the uninsured driver can pay and what the injured driver would be entitled to as if the uninsured motorist had proper insurance. [Wikipedia]
The first category of persons who may trigger an uninsured motorist provision consists of individuals who do not have liability coverage for the vehicle he or she is operating. In most states, it is a crime to be uninsured in this manner.
The next category consists of "hit and run" drivers or those drivers who flee the scene of an accident. When an individual flees the scene of an accident without leaving sufficient information to identify him or herself, the individual is considered uninsured for the purposes of an uninsured motorist provision.
However, that a positive ID of the license plates in a hit and run accident will often be considered by insurance companies sufficient information to identify the negligent hit and run driver. Such identification will often lead to the denial of an uninsured motorist claim, as insurance companies will often litigate the claim, bringing in the registered owner of the vehicle with matching plates, even when that person denies involvement in the accident.
So, if the vehicle was left behind - then it's a matter of there coverage for the over driver/vehicle or not. Too, it could be an issue of underinsurance coverage potentially.